The second one is a phone call, not an email. I'd refer to it as being 'forceful' or 'insisting.' I'm interested in setting up a meeting and sometimes the person I want to meet with, sees the email, but is buried under 100 more important things to do and doesn't get a chance to respond back.
Giving a quick, direct phone call
> 'Hey, I'd love to meet, I'm Kai, I emailed a few days ago, would meeting for an informational interview this Friday for 20 minutes work for you? (yes/no)'
can be a great way to get a direct response and fast.
What's the worst case? They say 'Sorry, I can't meet.' I'd rather have that direct answer than wonder about unreturned email.
My success ratio is high enough that I'm happy with this method. I don't have detailed records of how it's performed, but I'd guess that somewhere between 10% and 25% of the emails and calls I make turn into meetings. I'm really happy with that math.
Feedback is either 'Hey, we'd love to meet, how about <time>' or 'Sorry, I can't meet.'
If they say they can't meet, I either ask them if they know of a similar company they can direct me to that I can meet with or ask if they have time for one quick question (generally I ask what skill they're looking for in applicants and candidates).
I'm moving to Honolulu in November and I'm excited to double down on using this method again.